Almost Periodic Type Solutions Of Difference Equations

In this paper, we investigate the existence of almost periodic solutions and pseudo almost periodic solutions for difference equations.Chapter 1 considers the almost periodic solutions of difference equations. Section 1 introduces some definitions, symbols of almost periodic type functions and almost periodic type sequences; Section 2 introduces the exponential dichotomy for difference equations and some relating theorems. In Section 3, we study the existence and uniqueness of almost periodic solutions for linear difference equations x ( n+ 1)=A(n)x(n)+b(n)( n∈Z)and we proof two useful lemmas. Section 4 are based on Section 3 discuss the almost periodic solutions for nonlinear difference equations x ( n+ 1)=A(n)x(n)+F(n,x(n)),( n∈Z) and quasi linear difference equations x ( n+ 1)=A(n)x(n)+b(n)+εf (n,x(n),ε), ( n∈Z) .The last section presents the stability of almost periodic solutions for linear difference equations.Chapter 2 investigates the pseudo almost periodic solutions of difference equations. Section 1 mainly introduces some relating definitions and theorems for pseudo almost periodic sequences. In section 2, firstly, we discuss existence and uniqueness of pseudo almost periodic solutions for linear difference equations, and then using fixed point theorem ,we investigate the pseudo almost periodic solutions for nonlinear difference equations.